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" h110 FPLE COr'.
A TRIDENT SCHOLAR
PROJECT REPORT
UNO. 173
A Model of the Acoustic Interactions occurring
Under Arctic Ice "
ELECTE:-0ot1o ?I IM,
UNITED STATES NAVAL ACADEMY
ANNAPOLIS, MARYLAND
'I
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A MODEL OF THE ACOUSTIC INTERACTIONS OCCURRING Final 1989/90UNDER ARCTIC ICE. 6. PERFORMING ORG. REPORT NUMBER
7. AUTHOR(s) 8. CONTRACT OR GRANT NUMBER(a)
Roger R. Ullman, II
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United States Naval Academy, Annapolis.
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Underwater acousticsSea ice - Arctic regions
20. ABSTRACT (Continue on reverse aide if neceeary and Identify by block number)
Underwater sound interacting with the Arctic ice cover is reflectedfrom the plane surface as well as scattered due to small-scale roughnesselements and large pressure-ridge keel structures. Experiments modeled
the acousticrice interactions using burst transmissions fromomnidirectional underwater point sources. Floating acrylic plates wereemployed to represent the Arctic ice due to similarity in impedance - <A"' "
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characteristics and other physical properties to known ice values.Geometrical properties of the ice were accurately scaled in theacrylic by maintaining the appropriate wavelength ratios. Reflectionand forwardscatter effects were analyzed and compared with existingtheories for the Arctic. '
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U.S.N.A. - Trident Scholar project report; no. 173 (1990)
A Model of the Acoustic Interactions OccurringUnder Arctic Ice"
A Trident Scholar Project Report
by
Midshipman Roger R. Ullman, II, Class of 1990
U.S. Naval Academy
Annapolis, Maryland
A1
LCD Lj6nx G. Baker -Oceanography
Department
ChairpersontAccession ForNTIS GPA&X o tDTIO TABUnannotunced 5Just ification-
Availability Codes USNA-1531-2
1,A.vai &xd/o.'Dist Specal
ABSTRACT
Underwater sound interacting with the Arctic ice
cover is reflected from the plane surface as well as
scattered due to small-scale roughness elements and large
pressure-ridge keel structures. Experiments modeled the
acoustic-ice interactions using burst transmissions from
omnidirectional underwater point sources. Floating
acrylic plates were employed to represent the Arctic ice
due to similarity in impedance characteristics and other
physical properties to known ice values. Geometrical
properties of the ice were accurately scaled in the
acrylic by maintaining the appropriate wavelength ratios.
Reflection and forwardscatter effects were analyzed and
compared with existing theories for the Arctic.
2
ACKNOWLEDGMENTS
I am sincerely indebted to the following people:
Midshipman First Class Mark Watkins for his patient work
explaining the mysteries of TK Solver to a true computer
illiterate.
The U.S. Naval Academy Math Department for helping me
explore the bounds of complex trigunometry.
Mrs. Rachel Heberle, without whose help and artistic
influence I could never have completed my poster
successfully.
Mr. Bobby Bates and Mr. Clarence Woods of the Math and
Science Department for their superb workmanship in
crafting the acrylic keels used in this experiment.
My parents, Mr. and Mrs. Roger Ullman, for their support
despite not really knowing what I was doing, its relevance
to the real world, or why I would chose to dig myself so
deep a hole in my First Class year.
Midshipman First Class Matthew Simms for keeping me awake
through many late night work sessions and inspiring me to
3
achieve through the example of his own hard work for our
four years together by the Bay.
CDR M. P. Cavanaugh for subtly convincing me, without my
knowledge, that I really wanted to accept the challenge of
being a Trident Scholar.
Finally and without a doubt, most importantly, my advisor,
LCDR Leonyx G. Baker, for his unending support throughout
the entire project. His ability to excite my academic
interest and to discover perpetually the positive si 3,
whether it be a temporary setback in the laboratory or an
impasse in theoretical computations, is what carried me to
completion of this project and allowed me to graduate on
time.
4
TABLE OF CONTENTS
Abstract ............ ........................ 1
Acknowledgments .......... ..................... 2
Table of Contents .......... .................... 4
List of Tables .......... ..................... 6
List of Figures .......... ..................... 7
I. Introduction ......... ..................... .10
II. Acoustic Perspective of the Environment ......... .12
A. Open Ocean Acoustic Environment ............ .12
B. The Unique Arctic En.ironment ... .......... .13
C. Ice Characteristics ...... ............... .22
1. Ice Formation ...... ............... .22
2. Chemical and Compositional
Transformations ...... .............. 24
3. Physical Transformations ... .......... .25
D. Difficulty of Study ...... ............... .27
III. Experimental Procedure ...... ............... .31
A. Equipment Employed ...... ............... .31
1. Wavetek 20 MHz Function Generator ....... .32
2. Celesco LC-10 Hydrophones ... ......... .35
3. Hewlett-Packard AC Amplifier
Model 466A ....... ................. .35
4. Rapid Systems Real Time Spectrum Analyzer
Model R360 ....... ................. .35
5
5. Compaq DESKPRO computer and Amdek color
600 monitor ....... ................ .37
B. Description of Physical Models . . . ...... 37
1. Model of Smooth Arctic Ice ............ .40
2. Model of Arctic Pressure-ridge or Keel. .. 42
C. Experimental Technique ..... ............. .44
1. Initial Assumptions ..... ........... .44
2. Preliminary Computations ... .......... .45
D. Data Collection Methods ..... ............. .47
1. Reflection Data Collection ... ........ .47
2. Forwardscatter Data Collection .......... .49
IV. Acoustic Reflection ....... ................. .52
A. Theoretical Foundations ..... ............. .52
B. Wave Propagation at an Impedance Interface . . .54
C. Reflection at a Fluid-Solid Boundary ........ .59
D. Experimental Data and Conclusions .......... .67
V. Acoustic Scattering ....... ................. .79
A. Theoretical Foundations ..... ............. 79
B. Additional Environmental Parameters of
Import .......... .................... .79
C. Theories of Scatter Effects .... ........... .83
D. Forwardscatter Data and Conclusions .......... .87
VI. Summary of Findings ....... ................. .95
References .......... ....................... .99
Appendix .......... ....................... .102
6
LIST OF TABLES
I. Equipment List ..................... 34
II. Comparison of Arctic, Experimental andTheoretical Values. .. ............... 38
7
LIST OF FIGURES
Figure 1. Typical Open-ocean Sound VelocityProfile ........ ................... ..14
Figure 2. Open-Ocean Propagation Paths ........... .15
Figure 3. Arctic Temperature and SalinityProfiles ........ .................. ..17
Figure 4. Typical Arctic Sound VelocityProfile ... ................. ....... 18
Figure 5. Typical Arctic Propagation Paths ........ .20
Figure 6. Equipment Configuration ... ........... .. 33
Figure 7. Environmental Structure andLaboratory Model Counterpart ........... .43
Figure 8. Reflection at acrylic-waterinterface at 52.347 deg and61.523 kHz ....... ................. ..48
Figure 9. Forwardscattering Configuration ......... .. 51
Figure 10. Huygen's Principle As Applied ToReflection Phenomena .... ............ .53
Figure 11. Acoustic Interaction At A Liquid-Liquid Interface ....... ........... .56
Figure 12. Clay and Medwin Employing ComplexSound Speeds ....... ............... ..58
Figure 13. Reflection Coefficient for Acrylic-Water Interface ...... .............. .60
- -- -.-- - - -- ---- -- --
8
'Figure 14. Acoustic Interaction At A Liquid-Solid Interface ..... ............... .. 63
Figure 15. Reflection Coefficient for Acrylic-Fresh Water Interface .... ............ .64
Figure 16. Brekhovskikh ReflectionCoefficient with No Attenuation ......... .. 68
Figure 17. Brekhovskikh's Equation EmployingAttenuation and Complex Sound Speeds . . . . 69
Figure 18. Brekhovskikh's Equation EmployingAttenuation and Complex Sound Speeds . . . . 70
Figure 19(a). Reflection Coefficient for Acrylic/Fresh Water Interface (20.5 kHz) ....... 71
Figure 19(b). Reflection Coefficient for Acrylic/Fresh Water Interface (61.52 kHz) . . . . 72
Figure 19(c). Reflection Coefficient for Acrylic/Fresh Water Interface (80.08 kHz) . . .. 73
Figure 19(d). Reflection Coefficient for Acrylic/Fresh Water Interface (123.06 kHz). . . . 74
Figure 19(e). Reflection Coefficient for Acrylic/Fresh Water Interface (205.08 kHz). . . . 75
Figure 19(f). Reflection Coefficient for Acrylic/Fresh Water Interface (287 kHz) ...... .76
Figure 20. Huygen's Principle Applied ToScattering Phenomena ..... ......... .. 80
Figure 21. Mean Reported Values For Scatter Loss(Denny and Johnson, 1986) .... .......... .. 89
9
Figure 22. Environmental and TheoreticalTransmission Loss Data for a RoughSurface ....... ...................... 90
Figure 23. Environmentally CollectedReflection Loss Data .... ............ .91
Figure 24. Experimentally Derived ScatteringLoss Data ....... .................. 93
10
I. INTRODUCTION
Recent advances in the under-ice capabilities of the
Soviet naval forces include the ability to fire through
ice cover as noted by Covault (1984). LANDSAT images of
28 March 1984 indicate broken ice caused by Soviet
submarine operations. When linked with the desire for
increased exploration of fossil fuel deposits and the
determination of oil spill locations (Francois and Wen,
1983), reasons for renewed interest in Arctic acoustics
become apparent. This unique Arctic environment presents
a multitude of questions which are central to the study of
sound propagation, as well as a virtually noise-free
environment in which to seek to resolve them. Current
naval developments, relevant to both sonar operations and
underwater weapons performance, and technological
advances, enabling industry to access previously
unattainable natural resources, have simply highlighted
the importance of study in this region.
The experiments conducted in this study modeled the
acoustic energy-ice interactions using acrylic to
represent the Arctic ice. This substance was chosen due to
its similiarity in impedance characteristics and other
physical properties to known ice values.
Plane models simulating the large expanses of
relatively flat pack ice, as well as keel models to
ii
explore the interactions in the regions of pressure-
ridges, were employed. Reflection and forwardscatter
effects were analyzed as these account for the majority of
the energy in the Arctic acoustic budget and directly
affect long-range sound propagation.
A detailed investigation of the Arctic environment
provided the background for selecting an appropriate
representational forum. Experimental data were then
compared to existing theories for the Arctic,
demonstrating the relative merits of a variety of
equational modeling techniques.
12
II. ACOUSTIC PERSPECTIVE OF THE ENVIRONMENT
A. OPEN OCEAN ACOUSTIC ENVIRONMENT
Any study of Arctic acoustics inherently requires a
knowledge of typical open ocean sound propagation
phenomena. As acoustic energy propagates through a medium
it generates a density disturbance. The compressions and
rarefactions of the waves manifest themselves as increases
and decreases of the point densities along the path of
travel. Thus, the velocity (or celerity) of wave
propagation is a function of the density of the medium; in
the case of acoustic waves in the ocean, this medium is
sea water.
The density of sea water is a function of
temperature, salinity, and pressure; these three factors
determine the propagation characteristics as well.
Pressure increases linearly with depth, and the salinity
for any finite region of the open ocean can be assumed to
be roughly constant both vertically and horizontally.
Therefore, the dictating factor for sound speed
determinations in the "upper" or "operational" regions
(anything less than 1000 meters) becomes temperature.
The ocean's upper region is, in fact, composed of
several layers of differing temperature gradients, each of
which is prone to variation due to daily, seasonal, and
biological effects. At depths greater than 1000 meters
13
the temperature gradient decreases markedly as the water
temperature converges to a constant four degrees
Centigrade ('C). This temperature profile causes a
relatively constant, pressure-driven, positive sound speed
gradient underlying the volatile upper layers which, in
general, demonstrate a negative gradient. A common open-
ocean sound velocity profile, (a depiction of celerity
versus depth), is shown in Figure 1. The resulting
propagation pattern is demonstrated by Figure 2 and
exhibits an environmentally created waveguide or sound
channel. This is caused by the natural tendency of sound
to refract toward regions of slower sound velocity.
Attenuation of acoustic waves is affected by molecular
relaxations of magnesium sulfate, boric acid, and magnesium
carbonate present in the water (Mellen, 1987). These
effects are frequency dependent with higher frequencies
being more severely attenuated than lower ones.
Additionally, interactions with the water/air interface
and the sea floor account for losses as a portion of the
energy is transmitted into the adjacent media.
B. THE UNIQUE ARCTIC ENVIRONMENT
Acoustic wave propagation and scattering in the Arctic
pose several problems supplemental to those of the typical
open-ocean environment. The existence of unique
hydrothermal conditions is one factor. The surface layer
14
Typical Open-ocean Sound Velocity Profile
Seasonal thennoline
Moin thermocline
- - - - - - - - - - - -
4: 6,000 Deep isothermal toyer
9,000-
Figure 2. A typical open ocean sound vclocityprofile. (Urick, 1983)
Open-ocean PropAgation Paths
o
CY"0wtO X sac
~~~~~~~~"- Fiue..0dp0to0o y1.a pe ca
prpaato pah.(r Nk93
'N1
16
is at or near the freezing point, which for fresh water is
0* C and for sea water is -2' C. Additionally the layer
salinity is dilute, with values between 28 and 32 parts
per thousand (ppt), relative to a 34.7 ppt average in the
open ocean. This is due to the process by which the ice
precipitates salts after freezing. Below 50 meters,
however, a sharp salinity increase with depth is noted.
The next layer is termed the "Atlantic layer" and
ranges from 150 to 900 m. Temperatures above 0* C and as
great as 3" C may exist in this region. It is further
characterized by a relatively uniform salinity. The
combination of these factors with pressure effects
results in a monotonic increase with depth of density, and
thus acoustic speed, in this layer.
The bottom region, which may extend to dapths of 4846
m as in the Greenland Sea (Welsh et al., 1986),
demonstrates a highly uniform salinity, with values
between 34.93 and 34.99 ppt and a uniform temperature of
0 *C. Density in this layer becomes a function of
pressure. Figure 3 depicts the variation of the salinity
and temperature parameters with depth in the Arctic.
Figure 4 demonstrates the resulting typical sound velocity
profile.
Upward path refraction and, therefore, repeated
interaction with the overlying pack ice, results from
sound's propensity to travel toward regions of slower
17
Arctic Temperature and Salinity Profiles
TEMPERATURE - *C SALINITY- /oo
-2 -1 0 +1 30 31 32 33 34 3 0
20D- 0* 00
400. "400
60e . *0
800- - 00IOOL - 100
1000 C 4000
120D- 1200
• 150 * -1500
2000 00.0
250Q 2500
300J 3000
Figure 3. Temperature and salinity profilestypical of the Arctic environment(Urick, 1983)
18
Typical Arctic sounld Velocity Prof ile
0
-100STA8SLE ISOTHERMAL ZONE
RADIENT CONSTANT)
600 0.0165 /sec/m J
4 eoj
SLL
1.430 1.440 1,450 1,460 1.470 1,480 1,490
SOUND SPEED - /sec
Figure 4. A typical Arctic sound velocityprofile. (Urick, 1983)
19
celerity. In the profile commonly found in the Arctic,
where sound speed increaseo monotonically with depth,
this propagation pattern is known as "half-channel
ducting", a3 it demonstrates only the lower half of the
propagation pattern found in typical deep sound channels
in the open ocean (Figure 5). It is important to note the
difference in scales of the two axes in Figure 5; these
refractive effects occur over long horizontal distances,
and the waves do not come in contact with the surface as
frequently as might initially appear.
Long-range propagation paths which intersect the sea
floor essentially do not exist; thus, sea floor
interaction is a negligible cause of loss. Repeated sound
wave interaction with the surface is therefore responsible
for the majority of the losses incurred in the Arctic
acoustic energy budget. The existence of a liquid/solid
boundary at the surface results in an increase in observed
losses over values found in non-polar regions where the
junction is liquid/gas. At the sea water/air interface,
the reflection coefficient is nearly unity due to the
large disparity between the acoustic impedances of the two
substances, water and air. In the Arctic, however,
v:Ariations in the ice composition and incident angle of
the waves can result in values of the surface pressure
reflection coefficient ranging from -1 to 1. Understanding
the interactions that occur at the junction of the two
20Typical Arctic Propagation Paths 0
t')
CA,
Figure 5. A depiction-,of typical )Wctic propa-gation paths. (Diachok, 39074)
21
media and in the ice thus becomes crucial. This is
particularly true at the lower frequencies where
attenuation due to chemical effects does not play as key a
role and long distance propagation is possible.
Ice is a solid and can therefore support both
compressional and shear waves. This accounts for a great
deal of the increase in observed surface losses. However,
ice is both inhomogeneous in composition and not fully of
the solid phase; it is a lossy (a substance causing
attenuation or dissipation) multi-layered viscoelastic
medium, adding further complexity. A precise
deterministic equation for the amount of energy absorbed
by the ice, iwhat portion of the incident pressure returns
as a reflected wave, and how much energy is reradiated
later into the water does not yet exist (Browne, 1987).
Although extensive probablistic equations do exist for the qreflection at a liquid-solid interface where the solid is
upper-bounded by air, the lack of specific data concerning
the inhomogeneous ice composition and surface structure
precludes derivation of such an equation. Until a method
for determining this equation is found, an understanding
of reflection interaction at the interface will be
incomplete.
22
C. ICE CHARACTERISTICS
1. ICE FORMATION
Sea ice begins to form on the surface when the water
temperature is below the freezing point of -2" C.
Initially, minute spheres develop, forming individual ice
discs or platelets of 2 to 3 millimeters (mm) diameter.
Growth perpendicular to the principal hexagonal axis is
most rapid, thus the ice forms with this axis vertii.L
(Welsh, 1986). The orientation of the newly formed discs
is subsequently altered by water motion. Collisions with
other crystals ensure that they remain reasonably well-
rounded; fusion occurs when the platelets are brought into
contact with each other under pressure.
Although all of the discs begin to form in a similar
structural manner, the turbulent collisions to which they
are subjected result in mutation and realignment of the
initial axes of formation. Thus from the outset, the
newly forming ice cover is composed of a randomly oriented
crystalline structure. These weakly bound ice crystals
are termed "new" ice and may include "frazil" ice,
"grease" ice, "slush" and "shuga". They typically exhibit
a salinity greater than 5 ppt (Welsh 1986).
As this inital layer begins solidification, further
ice growth occurs on the bottom. The congealing ice is
now at least a few centimeters in thickness and is termed
-N mum&
23
"nilas" until it reaches 10 cm. Separation of individual
brine salts begins to occur due to gravity and temperature
effects at this point in the ice development. The
resulting mass of sea ice is vertically and horizontally
stratified and inundated with deposits of salts and air,
in addition to the chemicals that exist already within the
ice lattice structure (Vidmar, 1987).
The "young" ice stage follows and is composed of ice
from 10 to 30 cm. "First year" ice by definiton is any
ice that has developed in one growth season and may be
anywhere from 30 cm to 2 m in thickness. Preferential ice
crystal formation may exist at this stage based upon
under-ice current flow.
"Old", "multi-year" or "level" ice is defined as ice
that has survived one summer's melt season. It may be
thinner than two meters or as thick as five meters. Ice
in this final developmental stage contributes to pressure-
ridge structures (sails and keels). The depth of such a
keel is a function of the ice thickness. Multi-year ice
may be distinguished from first-year ice as it is more
rounded and generally thicker.
As brine freezes within the ice, it becomes
concentrated in small pockets, the majority of which have
been observed to be spheroidal (Bunney, 1974). These
spheres of increased salinity sea water (brine) may serve
as additional acoustic scattering centers. Regardless,
24
they disrupt the acoustic propagation by altering the
properties of the medium. What initially appears a rather
simple substance is highly inhomogeneous from the outset.
Variation in crystalline orientation, ice composition,
salt concentrations, and thickness all exist in the micro-
scale, resulting in a complicated, depth dependent,
anisotropic medium (Vidmar, 1987).
Icebergs are massive segments of fresh water ice that
have broken off or "calved" from the terminus of a glacier
or ice shelf. They may be distinguished by their size,
high relief, large freeboard and irregular shape. They
are present primarily in the Marginal Ice Zone (MIZ) and
are thus not of particular importance to the Arctic
acoustician.
2. CHEMICAL AND COMPOSITIONAL TRANSFORMATIONS
As time elapses, the effects of gravity and
temperature begin to be evident, and the newly formed ice
cover commences salt precipitation. Ice that formed more
quickly entrapped a higher concentration of the various
salts existing in the generating water, whereas slower
forming ice is of a lower salinity. Salt excretion causes
the surface water layer to increase in density and thereby
initiates mixing. This accounts for the nearly constant
salinity at depth with a partic'llarly dilute overlying
surface layer.
25
Ice may also form on the sea floor. This is referred
to as "anchor ice". The buoyancy produced by the
transition into the solid phase results in ascension of
the newly formed ice. Once it floats to the base of the
surface ice, it becomes frozen in place and incorporated
into the overlying Arctic cover. Sea floor sediments and
biological specimens thereby become consolidated within
the increasingly anisotropic surface ice layer
(Klieinerman, 1980).
3. PHYSICAL TRANSFORMATIONS
Not only is the ice inhomogeneous in composition and
structure, but it is not static. Movements of the entire
ice sheet are caused by winds, currents, waves and swell.
Gravity effects and temperature changes can cause cracking
of the surface. These movements further reorient the
internal air or brine structures and individual ice
crystals, adding to the inhomogeneity of acoustic property
distribution.
Numerous structures on the surface are created as a
result of movement, as the sheets break or crack and
subsequently override one another while being forced
together. Sails or "hummocks" form above the ice layer
and keels or "bummocks" below the surface. Ice movement
may be likened to the plate tectonic motion of the earth's
crust, for the edges of two ice sheets interact in a very
26
similar manner. Sail formation would be likened to
mountain development in this analogy. The difference
between the two processes is the lack of dissolution of
the supressed or subducted layer; the ice simply forms a
keel.
These pressure-ridge keels provide a large
population and a data base for detailed study regarding
size, spacing and frequency of occurrence. They are thus
of great interest to statisticians. Hibler et al. (1974),
utilizing visual measurements above the ice and submarine
underice profiles, developed a statistical model of
pressure ridge keel depths and spatial density. A
threshhold on the depth of structures that would be large
enough to be considered in the distribution was chosen,
ensuring that only veritable keels would be evaluated in
the data and that minute roughness elements would not
alter the sample population. The average depth for all
keels in the population below the cutoff depth of 6.1 m
was 9.6 m with an average width of 36.2 m and a median
distribution of 4.3 keels per km (Hibler et al., 1974).
Floe collision forms fields of random ice rubble in
addition to the more simple vertical ridge structures.
Further complexity is caused by gaps that develop in the
Ic- sheet- "Leads" are ca- in the ice resembling
rivers. "Polynya" is the term denoting large holes
resembling lakes. These expansion formations add multiple
27
edge surfaces and combine with the already present surface
roughness factors to cause a highly complex acoustic
environment. Finally, a varying snow cover adds an
additional layer of unique acoustic properties and thereby
further complicates analyses.
D. DIFFICULTY OF STUDY
The Arctic environment presents a broad range of
parameters to the acoustician and a plethora of variables
not present in the open ocean. It has thus been a region
of intense study, an example of which is the multiple
MIZEX (Marginal Ice Zone Experiments). There are,
however, numerous difficulties encountered when seeking to
study the Arctic. The primary and most obvious limitation
to scientific research is the Arctic environment itself.
Severe weather patterns as well as the extremes in
temperature experienced there make the development of any
insitu measurements particularly difficult both from the
standpoint of human and equipment factors (Welsh, 1986).
Its remote location and harsh climate render study
extremely difficult.
28
Despite these obstacles, the region under the pack
ice of the Arctic is one of the quietest acoustically, due
to the lack of sea state, biological, and shipping effects
that all contribute to ambient noise in non-polar regions.
Further, high frequency noise is quickly attenuated due to
the scattering effects of the rough under-ice surface.
The more easily accessible Marginal or Seasonal Sea
Ice Zone (MIZ or SSIZ) is, however, among the noisiest
regions on the planet acoustically. All of the typical
contributing factors to ambient noise exist here with
several additions. Cracking and buckling ice, wave-ice
floe interaction and noise caused by the movements and
collisions of the ice all add to the cacophony.
Scattering due to submerged ice keels clutters the
environment further. Surface ice sails and submerged
keels alter the ice thickness; the geometric and thus
acoustic properties of the ice change. Minute surface
roughness factors of Arctic sheet ice contribute to the
complexity of the environment and to scattering. Losses
may also result from an air layer trapped between the sea
and the ice cap.
A zone of "partial freezing" up to 20 centimeters
thick in which the sea water has properties of both solid
and liquid is another region of attenuation. The acoustic
chain of events that occurs between the solid ice sheet
and the underlying liquid sea'water in this "fluid" or
29
"colloidal" region has yet to be fully explained (Bunney,
1974). This region of partial freezing lends itself well
to a multitude of questions regarding its structure,
formation, resulting effects on the acoustic environment,
etc.
Finally, the transportation of ice samples, which
would alleviate some of the environmental difficulties,
has proven to be rather infeasable and the subsequent test
results somewhat inaccurate due to the chemical changes
that occur as the ice is subjected to temperature and
gravity variations. Drainage of brine during "coring" (or
collection) of the ice samples and surface melting during
experimentation alter the properties, as well, rendering
transportation rather inutile (Vidmar, 1987).
A numerical model for the acoustic reflection in the
Arctic region, particularly at "lower" frequencies (less
than one kilohertz), where present model results tend to
diverge from the environmentally derived data, may help
obtain a more complete understanding of sound propagation
(Mellen, 1987). Additionally, the development of a model
for prediction of the ice sheet's characteristics, depth,
and acoustic properties based on easily discernible
factors such as temperature, salinity and pressure is
sought. This will lead to a more complete acoustic model
of the Arctic region throughout all frequency ranges.
30
A detailed understanding of the phase change of sea
water may present new insights into the sound patterns
observed in the colloidal region. Likewise, the
propagation of acoustic waves through the ice, either as
compressional or shear waves, provides another avenue for
attenuated energy and deserves attention. Reradiation
from the solid supplements scattering and signal
interference. There are thus a myriad of additional
variables with which the acoustician must be concerned
when working in the Arctic environment additional to those
of import in the open ocean basins.
31
III. EXPERIMENTAL PROCEDURE
Ice was modeled using acrylic plate in an effort to
explore the interactions that occur under the Arctic pack
and thereby gain further insight into long-range
propagation phenomena. These scale models were floated in
two large tanks and impinged upon by burst emissions of six
different frequencies. Reflection and forwardscatter data
were then collected.
A. EQUIPMENT EMPLOYED
Two different tanks p:ovided the environment for this
experiment. The first was a 353.3 liter (L) tank with
dimensions of: length - 180.5 cm, width - 43.5 cm, depth -
45 cm. The second tank employed had a volume of 11.6 kL
and dimensions of: length - 3.2 m, width - 2.8 m, depth -
2.3 m. The use of two different sized tanks expanded the
range of angles that were geometrically feasible, thereby
enlarging the final data base.
Neither tank was anechoic or acoustically isolated.
The smaller tank was subject to 60 Hz signals from nearby
laboratory equipment which added undesired noise to the
environment. The larger tank exhibited far more ambient
clutter. This 11.6 kL tank, bolted to the foundation and
connected to a series of pumps and motors, is acoustically
coupled to a plethora of noise sources. Although this
32
ambient noise should have had little bearing on the data,
as the frequencies with which the experiment was concerned
were a minimum of three orders of magnitude larger, it is
important to note that this noise did exist.
A filter was not used to remove this low frequency
noise, since burst or pulse emission was employed in the
model. A burst is formed from a sum of frequencies as per
the Fourier theorem; removing any of the lower frequency
components would have altered the received pulse.
Figure 6 illustrates the equipment organization
employed for the experiments. Equipment utilized is listed
in Table I. A more detailed explanation of specific
equipment capability and usage proceeds below.
1. Wavetek 20 MHz Function Generator Mode_ 191
The Wavetek function gene?.-ator operates in a frequency
range of .002 Hz to 20 MHz. It is capable of sine,
triangle, and square wave output ranging from 1.5
millivolts peak to peak (mV~P) to 30 Vp-p. It supplies a
peak current of 150 milliamps that may be continuously
varied over an 80 deciBel (dB) range.
The function generator served as the source of the
acoustic energy and was primarily employed in the double
pulse mode. This mode emits a signal of two complete
cycles at a given frequency when the trigger is activated;
this will be termed a pulse or burst. The manual trigger
33
Equipment Configuration
WAVETEK FUNCTIONGENERATOR
0 00 0 / SOURCE RECEIVER
HEWLET PACKARD 0AMPLIFIER
[[IIi)ANALOGDGIARAPID SYSTEMS SOFTWAREIN COMPAQ COMPUTER
Figure .6. Equipment configuration for theexperiments
34
TABLE I
EQUIPMENT LIST
Abbreviation Nmenclature
Amp-i3fier Hewlett Packard AC Amplifier,Model 466A
Source or Receiver Celesco LC-10 Hydrophone
Function Generator Wavetek 20 MHz FunctionGenerator, Model 191
Spectrum Analyzer Rapid Systems Real TimeSpectrum Analyzer, Model R360with Data Acquisition andAnalysis Package
Computer/Oscilloscope Compaq DESKPRO computer and
Amdek Color 600 monitor
Analog/Digital Converter Rapid Systems 4X4 DigitalOscilloscope rctripheralanalog/digita.. converter
35
configuration was utilized which permitted the operator to
control the frequency of pulse propagation and allow
adequate time between emitted signals for echoes in the
tank to dissipate.
2. Celesco LC-10 Hydrophones
Two Celesco LC-10 Hydrophones were used as omni-
directional source and receiver in the laboratory. Their
lightweight highly portable nature facilitated adjustments
within the tank. The 40 cm of connection cord immediately
adjacent to the hydrophones was encased within a plastic
tube and marked with centimeter gradations to ensure proper
hydrophone depth, orientation, and stability once placed.
3. lFwlett Packard AC Amplifier Model 466A
A Hewlett Packard AC Amplifier was employed to enhance
the return signal from the receiving hydrophone before
being routed for processing into the Real Time Analyzer.
It is capable of 0, 20 and 40 dB signal gain and was
utilized in the 40 dB gain configuration primarily.
4. Rapid Systems Real Time Spectrum Analyzer Model R360
The Rapid Systems Real Time Spectrum Analyzer with the
4X4 Digita! Osciloscope peripheral, R300 Digital Signal
Processing Interface Board, and R360 Real Time Spectrum
Analyzer software was installed in the Compaq DESKPRO
36
computer. It provided the heart of the signal acquisition
and analyzation. The frequency spectrum capabilities
permitted calibration of the function generator frequency
accuracy. The saving mode allowed the pulses to be
recorded onto 5-Y4" floppy disks for later examination.
Analysis techniques are described in the following section.
The software package enables ?,,-,n time and voltage
readings of the wave signals. Sampling and display time
can be altered, essentially compressing or expanding the
waveform information. The 40 microsecond (Jsec) mode (the
smallest sampling interval) was used throughout. Several
trigger options are available; however, only the digital
mode was used in this experi."ent. The digital
configuration begins collection of the 2048 data points at
0 volts and the first indication of a positive slope (i.e.
as soon as the emitted pulse was triggered). A viewtime
delay may be entered; this option was not chosen in order
to allow the operator to view the emitted and reflected
pulses immediately. Gain of the channels can be
individually manipulated to facilitate viewing, and there
are various options for summing the channel displays. The
variable pulse or "non-summing" option was chosen, as this
permitted separation and independent viewing of the source
pulse from those received.
37
5. Compaq DESKPRO computer and Amdek Color 600 monitor
The Compaq computer housed the Rapid Systems software.
The Color 600 monitor served fundamentally as the
oscilloscope in this configuration and enabled viewing of
the data collection.
B. DESCRIPTION OF PHYSICAL MODELS
Acrylic was chosen as the medium for the model due to
its similarity to the known parameters of Arctic ice.
Table II presents a comparison of values for the acrylic
employed in the laboratory and those reported in the
literature for typical Arctic ice.
The compressional wave speed (cp2), acoustic impedance
(p2Cp2) and bulk modulus (E) of the acrylic all lie
centrally within the range of typical Arctic values. The
density of the acrylic (P2) is approximately 25% too high
and the shear wave speed (c.2) is roughly 10% too low. The
rigidity or shear modulus (G) is low by a factor of three,
but the remainder of the parameters of the acrylic show
good agreement with the ice values when scaled for the
appropriate wavelengths. Medwin et al. (1988), Denny and
Johnson (1986) and Browne (1987) have previously
demonstrated the effectiveness of acrylic as a modeling
medium for Arctic ice.
38
c to W T - m m~ o o4 n tol 0o 0,>. CD)q 0
O'o mo HO O V%D) C4n 04% -4a Co C-4r
MI 1 C14t C>to -44H
U!
Ao M I. 0
M V o 0 *v> c0vo
E-4~ CD Cl CD O 0 CCO C'4 m
z
E-4 1 N 0> r--z 40 on %0 RW
H it)
w 0c ci a%)00) .- -
H> v
0D r- r-4 r-4 If
0 $.4
z0 4i 1 C ,
a) H 0 ~
r-) 44~3 44 Q.4cq C
(d4 0 ~ (d 0 Hj 04 H~
o ) o o', -H HA4-> Q)Wq c >1
w ~ HO W ')to V
H C,4 0" cp 0. a-
3 9
N' N -('4 C) N. 1q, co
0l -- 0
(9) co 0 r C)- o
10-
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Cr)q 00
04 0)
4 p (d o U
to4 Cr) 0u0E-4Vo oo Qin w Ac4o
*Q V *. >(29.4
C9) CH * -4(I
H~H
*dD)cO'O 0~4
040)) H
44H a) Cr o n U) . *) 0U )~ Q0 4r d) -H toCi0Q 4 a)
44 ) *1 W'. C4 :3 caJ~4 0L
co o it 0.4 4~ *)r0
.' M C4 1) Cr2)oV-4 0 H4 4 ->0t :-J * 0. ('4 H(A (d
i5 ,I . I. 1 4 - d >
0C"m4) H E-4 4- t 1
4J -i 0 W~' * a)S .0 :
H d *v Hr IdV4 0 3-
(pi 1. 0 -4 0 e '.0 U >0
ro rH W 0)Z D a 0 atA > U - -)> 0 o 0) *,4)o ~~~ .- G) to Pl H H 0 .0
C;- Cl) 14 C4 C
40
1. MODEL OF SMOOTH ARCTIC ICE
Acrylic of .63 cm thickness (1/4 inch) was employed
to model the Arctic ice pack. Three separate pieces were
used: a 20 cm by 40 cm rectangle, a 40 cm square, and a
60.5 cm by 81 cm rectangle. The use of three acrylic
pieces along with two different tank environments permitted
an increase in the range of geometrical configurations
possible and, therefore, data collection over a broader
range of angles, which generated more insightful results.
Once a model was found which accurately reproduced
the physical parameters of the Arctic, it was necessary to
scale the model length and laboratory wavelengths to
simulate Arctic frequencies of interest. As indicated, the
choice of acrylic ensured close correspondence of the
acoustically significant properties. The subsequent
concern was assuring that the ratio of plate thickness (h'
to acoustic wavelength (lambda) be the same for the acre'"
as for the Arctic region being modeled. The accuracy or
this scaling technique has been successfully demonstrated
(as previously cited) and requiras only that this ratio be
maintained for the model to be an accurate environmental
representation.
Therefore, if a typical Arctic level ice thickness is
taken to be 2.5 m, then .0063 m acrylic (1/4 in)
41
corresponds to a scale of 396.8 : 1. Thus, for the six
frequencies chosen, fice= facryiic/ 3 9 6 - 8 and:
facrylic = 20.51 kHz represents fice = 51.68 Hz
facrylic = 61.52 kHz represents fie. = 155.05 Hz
facrylic = 80.08 kHz represents fic. = 201.81 Hz
facrylic = 123.05 kHz represents fice = 310.11 Hz
facrylic = 205.08 kHz represents fice = 516.83 Hz
facrylic = 287.00 kHz represents fice = 723.29 Hz
These frequencies were chosen with attention to the
harmonics of the two prevalent operational frequencies, 50
and 60 Hz. They are also distributed over a fairly large
range in order to permit investigation of the existence of
frequency dependence for reflection and scattering
phenomena. The first, third, fourth, sixth, tenth, and
fourteenth harmonics of a 50 Hz signal are fairly closely
represented. The fifth and twelfth harmonics of a 60 Hz
signal also occur. The 123.05 kHz frequency is of
particular interest, as it is a close representation of an
important harmonic of both signals. The 287 kHz frequency
also closely represents a dual harmonic.
Although the acrylic density was greater than that of
the water: surface tension forces were sufficent to sustain
its flotation. This was fortuitous as it enabled the
experiments to proceed without the addition of any
42
extraneous substances that would have been solely for
support and had no similarity to Arctic structures.
2. MODEL OF ARCTIC PRESSURE RIDGE OR KEEL
The pressure ridges present in the Arctic were modeled
in the laboratory for scattering data collection. Two
separate acrylic keel models were constructed (widths 20 cm
and 40 cm) again to expand the range of geometrical
configurations (Figure 7). The contribution of the sail to
scattering effects is considered negligible (Browne, 1987),
thus a sail was not added to the keel model.
Maintaining the same thickness-to-wavelength ratios
that were employed for the plane acrylic surface, this
model represents a keel of depth 9.12 m and 33.5 m width as
indicated by the values in parentheses in Figure 7. This
is a standard value for an Arctic pressure ridge and agrees
with values reported by Hibler et al. (1974) and previously
cited.
The two pressure-ridge keels were constructed by the
gluing of a triangular acrylic keel section to the plate
acrylic sheet. This was performed using Comstik Plexite
Cement 1 adhesive manufactured by the Rohm and Haas
Company. As the scattering effects of the acrylic keel are
the interactions of interest, any alteration of the
acoustic properties of the acrylic by this minute glue
layer were ignored.
43
Environmental Structure and Laboratory Model Counterpart
9. 12 m
33.5 m
4.20 or .40 m
.023m% % (9.12)
.0845m
(33.5)
Figure 7. A schematic diagram of the laboratorymodel and a depiction of the structureit represents with appropriate dimen-sional values.
44
C. EXPERIMENTAL TECHNIQUE
1. INITIAL ASSUMPTIONS
It was necessary to make several assumptions at the
outset of the experiment to simplify the model.
Attenuation effects in the fluid were determined to be
negligible, due to the similarity of path lengths between
the direct and reflected pulses. Any loss occurring would
affect the transmission of both waves virtually equally so
that these effects can be factored out.
Additifenally, homogeneity of the acrylic properties
was assumed. This, of itself, is a valid conclusion, but
it contradicts the known anisotropy of Arctic sea ice which
the model represents. Likewise, the salinity and
temperature structure of the sea water layer immediately
adjacent to the pack ice demonstrates vertical variation
due to salt precipitation and mixing effects (see Figure
-). The homogeneity of the laboratory model again does not
correspond to the environmental values. These limitations
in the model were noted but deemed negligible when studying
solely the interactions that occur at the interface of the
two media.
The final assumption was that the experiment occurred
in the acoustic far field. This condition reduced the
model to plane waves, thereby simplifying computation.
This assumption requires that the separation between
45
hydrophones be sufficient to allow for curvature effects in
the propagating wavefront to be negligible. This is
usually assured by satisfying:
kr >> 1
where k is the wave number (2nf/c) and c is the speed of
sound in the medium, f is the frequency of the waves and r
is the separation of the source and the point of concern in
meters. In order for the product kr to be considered much
greater than one, the condition is placed that kr should be
greater than 11. Taking a value of kr equal to 11, c =
1500, and solving for r using the lowest frequency (f =
20.51 kHz), (which will cause the maximum value for r
within which the experiment would still be operating in the
near field), generates r = .128 m. Thus, in order for the
experiment to be considered in the far field r (the
separation between source and receiver) must be greater
than 12.8 cm. With a minimum hydrophone separation in
excess of 20 cm, this value was exceeded throughout the
experiment. The far field assumption is therefore valid.
2. PRELIMINARY COMPUTATIONS
Initial calculation of sound speed in the water and
acrylic both theoretically and experimentally was essential
for the remainder of the computations. Wilson's simplified
equation:
46
c = 1449.2 + 4.6T - .055T 2 + .00029T 3 +
(1.34 - .01T) (S-35) + .016z
where c = sound speed (m/s) T = temperature ('C)
S = salinity (ppt) z = depth (m)
presented the theoretical value for sound speed of water
(Clay and Medwin, 1977). When combined with laboratory
measurements and literature parameters, a value for sound
speed in water of 1500 m/s was determined to be reasonable.
Theoretical computation of the acrylic sound speed was
difficult due to the lack of available acoustically
oriented data. Thus, fundamental equations were employed
with an iterative solving process to acheive a sound speed
value of 2201.09 m/s which compared favorably with
laboratory determinations. The mathematical process
utilized is detailed in the Appendix.
Pulsed omnidirectional signals of two cycle duration
were transmitted and the reflection was identified and
isolated employing a precalculated time reference "window".
Measurement of precise hydrophone placement relative to the
boundaries of the tank and knowledge of the value of the
sound speed allowed this parameter to be computed. A
sirmple series of trigonometric and velocity equations were
used. The Appendix also discusses more fully the manner in
which this time window was determined.
47
Figure 8 is a sample return with annotated pulses. It
is indicative of the type and format of data collected. It
also demonstrates the specific parameters which were chosen
for data collection during the experiment.
D. DATA COLLECTION METHODS
1. REFLECTION DATA COLLECTION
Once the variable channel mode had been selected and
all extraneous or residual pressure phenomena in the tank
had subsided, the trigger was activated, emitting the two
cycle pulse as described above. This was viewed on the
upper trace of Figure 8 (denoted channel B) while all
reflections were displayed on the lower trace as shown in
Figure 8 (channel A).
The direct path and reflected pulse were isolated
employing the time window parameters determined as per the
Appendix. The direct path was obviously the first to
arrive; the desired surface reflected path was isolated
from the remaining "noise" reflections. The Rapid Systems
software gives time and voltage output for both channels at
distinct time positions along the waveform. These
locations are chosen by means of a cursor along the
Measurement was taken of the peak voltage for the
direct path pulse and the reflected pulse. The direct path
48
....._ ... ..... ..*" . .. .. . . . . . .... 40 II C ."
-me-
I z../..-I
- - - -. . . . . - . . . . . . .°
- .- .... - --- - - -# ... . ' 5 ...... / /
2= - :='
... .. .. ... ..... . . ." -. -
- - -. -. - -
. . .. ..... 1
......... .....------------------ - .
,_s~ _ ° .
fAft
- - - - - - -....
z -a*_
C.- , ,, . . .. ___ .
-., - -o - - - - - -0 .
U - -- - -
-a-
- - Ii- Ab
with attosidctn-h
Vechoe of Import A
-= O wCn WV.-ASLa
;-- _8 a k f - C ,O
. -9dem - a
Figure 8. Tpia-----fr-aa olet o
wit anoain indcain the
__echoes of import
49
value served as the denominator for the reflection ratio
and the numerator was the peak voltage amplitude of the
reflected pulse. Thus, the ratio generated is a pressure
reflection coefficient. This method inherently has some
limitations due to the stepping mechanism of the voltage
reading system. The software proceeds along the waveform
in increments of 2 microseconds. It is therefore possible
that the actual peak values of either of the signals might
have occurred in between the samplings and been overlooked.
This possibility was accounted for by the performance of a
minimum of six "runs" at each geometry (i.e. each angle of
incidence) for each frequency and the computation of an
average value for both direct path voltage and reflected
voltage. This average value serves as one "trial" and
corresponds to a specific voltage and specific angle of
incidence. The voltage ratio (representing the pressure
ratio) was then plotted as the pressure reflection
coefficeient.
2. SCATTERING DATA COLLECTION
The initial goal was collection of both forward and
backscatter data from the acrylic keel models. One
hydrophone was placed adjacent to and in contact with the
source and a second was placed on the opposite side of the
acrylic, equidistant from the keel and at the same depth as
the source. Due to the ringing that occurs from the
50
magnitude of the power of the emitted burst, the hydrophone
was rendered inutile for reception of backscattering data.
Some separation of the source and receiver hydrophone is
required and this precluded obtaining backscatter data due
to a desire to maintain appropriate angular alignment.
Forwardscatter data was collected in a manner similar
to that followed for the reflection experiment. A diagram
of the model configuration is found in Figure 9. A minimum
of twenty runs was performed for each trial. The value at
each trial represents the pressure scattering coefficient,
a ratio of forwardscatter pressure to -irect path pressure
at a given angle of incidence. It is, however, more common
to work with grazing angle when dealing with scattering
data. The grazing angle is the angle of impingement
measured from the horizontal, or the complement of the
angle of incidence. Thus, data are presented in this
format.
52
Forwardscatteriflg configurationl
IF~
% 0)
Hydrobone nd acylic odelcn-,-oraionfor athringforardcatejng Clat
52
IV. ACOUSTIC REFLECTION
A. THEORETICAL FOUNDATIONS
Initial understanding of wave propagation may be
gained through a study of Huygens' principle. This states
that each discrete unit area on an advancing wave is
considered a re-radiating point source of spherical waves.
The outer surface that includes these new "wavefronts"
constitutes the front of the new wave (Figure 10).
Huygen's theory may be expanded to explain the
reflection of a wave at a plane interface. The wave
construction proceeds with the supposition that there
exists an "image" source at a distance beneath the surface
which is equivalent to the distance between the surface
and the real source. The real wave front is assumed to
travel into the image region as in Figure 10(a).
Concurrent with the propagation of the real wave, the
image wave originates at the image point (Figure 10(b))
and travels towards real space, entering it to become the
reflected wave. The reflected wave will have an intensity
of RII where I is the intensity of the incident wave and
R, is the intensity reflection coefficient, which
represents that fraction of the intensity of the incident
wave that is reflected. The reflected wave continues to
propagate in the real region in the same manner as the
original wave (Figure 10(c) (Clay and Medwin, 1977).
53
Huygen's Principle As Applied To Reflection Phenomena
/ / % \I Il
100wae a 0n t i
rgon (nto the "iale"ren.ect.
(Clay and Iedwin, 1977)
54
In the study of acoustics, it is common to deal with
large distances from the source. In this region, termed
the far field, the curvature of the wave is relatively
small, in fact negligible. Thus, the wave may be
considered a plane phenomenon. The mathematical basis for
and limitations to this assumption are described in the
Procedure chapter.
The use of ray theory further simplifies acoustic
energy analysis. A line constructed perpendicular to the
wave fronts is traced as a ray rather than tracking the
paths of individual waves (Figure 10(a)). It is with
these theoretical assumptions that the discussion shall
proceed.
B. WAVE PROPAGATION AT AN IMPEDANCE INTERFACE
When acoustic waves strike a discontinuity of
acoustic impedance (Z), whether it be caused by a change
in medium density (p) or sound velocity (c) or both, the
propagation is altered. At the interface of a plane
smooth boundary, part of the energy is transmitted and a
portion of it is reflected. The angle at which the energy
is reflected is identical to the angle of incidence. The
transmitted wave, however, follows Snell's Law:
{sin(@j)/cj} = {sin(8 2)/c2} (1)
55
where cl and c2 are the sound speeds in the respective
media, 61 is the angle of incidence in medium 1 measured
from the normal, and 62 is the transmitted angle in medium
2, also measured from the normal.
Figure 11 represents the interaction at an acoustic
impedance interface. Notice that 01, the incident angle
is equal to 0r the reflected angle. Also note that in
employing Snell's Law, one can determine that the sound
speed of medium 2 must be lower than that of medium 1.
This fact is derived from the refraction of the
transmitted ray toward the perpendicular and the decrease
in 62 from 61.
Acoustic waves travel as a pressure disturbance as
previously indicated. The value of the reflection
coefficient will therefore be the ratio of the reflected
pressure amplitude to the incident pressure. In order to
calculate this ratio two boundary conditions are required.
They are:
1. Continuity of Pressure: The interface does not
have an excess pressure on one side or the other. This
requires that the algebraic sum of the incident and
reflected pressures be equal to the transmitted pressure
at the intorfpt-.
2. Continuity of the normal component of the fluid
particle velocity! The two media maintain contact at the
56Acoustic Interaction At A Liquid-Liquid Interface
TRANSMITTED- GOMPRESSIONAL
- PAY
22 p2c2
INCIDENT RF.CE
R AY RAY
Pigure 2s 1L~U.L AC;%a-vn-i at. the interfacebetween two mnedia of differing acousticimpedances. A portion of the energy istransmitted into the new inedium, theremainder is reflected back into themedium of origin
57
interface as the signal reflects and passes through the
interface.
Once these conditions are satisfied, the ratio of
reflected to incident pressure (R;) may be determined.
This is:
Rp = P2 c2 - Pc 1 Pr (2)
P2 c 2 + PI c1 Pi
where pi and p2 are the densities of the respective media,
Pr is the amplitude of the reflected pressure and Pi is
the incident pressure amplitude. Taking into account
oblique angles of incidence leads to:
= P2 c2 cos (81) - P1 c1 cos (e 2 ) Pr= - (3)
P2 C2 COS(8 1) + P. cI cos(0 2) Pi
A plot of equation (3) with typical acrylic values is
shown in Figure 12. These values are cl = 1500 m/s, c2 =
2201.09 m/s, p, = 998.503 kg/m3 , and P2 = 1189.8 kg/m 3 .
As long as c 2 < c1, the value of (c 2 /cl) sin (6 1 ) will
be less than one for all values of e. However, if
C2 > cl, as is true in the Arctic and the acrylic model,
the phenomenon of "total reflection" occurs. A critical
angle (@orit) is reached when:
sin(Ocrit) = (cl/c 2) (4)
C42
- 0-
>~W0.M
-C
0
~~~:,~~T %AP ~ou 3 C)(
Figure 12. The theoretical pressure reflectioncoef ficient at the acrylic-waterinterface emiploying equation (3)
59
At angles greater than the critical angle, the signal
reflects with a pressure reflection coefficient of one and
an associated phase change. To indicate this and to
resolve ambiguity caused by the value of (c2/cl)sin(01 )
exceeding one, complex notation is employed and results
in:
RP = P2 c 2 cos(()) + i p, cl b2(5)
P2 c 2 cos(6 1 ) - i p, cl b2
where b2 = ± i cos(e 2 ) = 4 (c 2 /c 1 )2 sin2(81 ) - 1
(Clay and Medwin, 1977). This equation is depicted in
Figure 13 employing typical model values as in Figure 12.
C. REFLECTION AT A FLUID-SOLID BOUNDARY
In the Arctic a more complex case is of concern.
This region experiences a plane wave incident upon what is
normally modeled as a plane boundary between a liquid
halfspace and a solid one. Obviously this liquid-solid
model is not as simple as the reflection at an interface
between two fluids differing solely in density or sound
speed, yet still not as complex as the Arctic in which the
ice is actually a rough-surfaced lossy multi-layered
viscoelastic medium upperbounded by a gas. Unlike the
liquid or gas, the solid phase can support shear or
transverse waves; this adds another dimension to the
60
CS-
~-Z4
-r
-4OC
o2
C-,-E-
0-44
o
f44CC)
o
-49
94~Z
derived from equation (5) when using
laboratory values
61
increasingly diverse reflection picture. When a
compressional wave in a fluid is incident on an elastic
solid, part of the energy is reflected back into the
liquid medium, part is transmitted as a compressional wave
in the solid, and part is transmitted as a shear wave in
the solid.
At the liquid/solid boundary, the vertical
displacements in the two media are equal, the vertical
stress is continuous, and the tangential stress in the
solid vanishes at the interface because the non-viscous
liquid (which water is assumed to be) does not support
shear waves. Snell's Law remains applicable and may be
expanded to:
{sin(61 )/cl = {sin(8 2 p)/Cp2} = {sin(e 2s)/Cs2 } (6)
wheie cp2 is the compressional sound speed in medium 2,
C.2 is the shear sound speed in medium 2, 62s is angle of
shear wave propagation in medium 2 measured from the
normal and 8 2p is angle of compressional wave propagation
in medium 2 measured from the normal. This, according to
Clay and Medwin (1977), (given the same boundary
conditions as the liquid-liquid interface), alters the
equation for the pressure ---------- --- f---n
equation (7):
62
R= 4C282a2 + (522 - a2)2 - (pl/p2) (T2 /T 1 ) (w4/c,24)4T 25 2a
2 + (522 - a 2 )2 + (pl/P2) (T 2 /T 1 ) (w4 /C3 24 )
where simplifying by algebraic manipulation leads to:
w = 2xf (f is frequency in Hertz)
a= (w/cl) sin(0 1 ) -r= (w/c 1 ) cos(0 1 )
T2 = (w/Cp 2 )1- { (Cp2/Cl) sin (B1) }2]X
82 = (W/Cs 2 ) 1 - { (Cs 2 /Cl) sin (@1) }2]X
This form of the reflection coefficient takes into account
the additional losses observed due to the propagation of
shear waves, which the liquid is unable to support.
Figure 14 demonstrates the ray geometry in this
environment, the difference from Figure 11 being the
transmission of a shear wave in addition to a
compressional wave.
Above the critical angle it is necessary to utilize
complex notation. This results in a plot for the pressure
reflection coefficient in terms of incident angle (with
the acrylic model values) as shown in Figure 15. Note
that the value of the coefficient is unity both at the
critical angle and at normal incidence. Values of the
reflection coefficient for incident angles less than thecritical angle (crit) are affect d by ltbrAtions of the
compressional wave speed (cp), whereas those greater than
8 crit are affected by variations of shear celerity (c.).
63
Acoustic Interaction At A Liquid- Solid Interface
I "R SMITTEDSHEAR RAY
O2s02t TRANSMITTED
COMPRESSIONAL
- RAY
Z2 .p2c2
21 pici
INCIDENT REFLECTED
Or RAY
Figure 14. Acoustic interaction at the interfacebetween a liquid and solid. Energy istransmitted as both compressional andshear waves as eil as reflected
64
oC =
- a'0 03
~~P4
[-4n
r4
Cq
P .4 . r .4 .
o0
E-
44-
o
¢.))
Figure "15. A plot of the theoretical pressurereflectio.p coefficient obtained fromequation (7) when complex celeritiesare used above 6,,rit
65
Although frequency may be factored from Clay and
Medwin's equation (7), z frequency dependence is noted
from the experimental data; this is attributed to acoustic
energy attenuation in the media. Velocity and
attenuation in solids change with frequency according to
Vidmar (1987) and McCammon and McDaniel (1985) although
these conclusions were not obtained by Langleben (1970)
for sea ice. Attenuation effects are normally modeled
mathematically by the utilization of complex sound speeds.
To generate a complex celerity, the real sound speed
c is redefined as c = c' + ic" with both c' and c" real
numbers. Subsequently, c' and c" are defined as follows:
c' =c/ [ + (c/k)2] and
c" = [c (a/k)] / [I + (a/k)2] (8)
where k is the wave number (2nf/c) and a (alpha) is the
compressional attenuation coefficient (Clay and Medwin,
1977). The shear attenuation coefficient will be
represented by P. The attenuation coefficient itself
often varies with frequency; McCammon and McDaniel (1985)
report attenuation coefficients in ice of:
= .06f(-6/T)2/3 dB/m kHz and
= .36f(-6/T)2/3 dB/m kHz
66
where a is the coefficient for compressional waves, P is
the coefficient for shear waves, f is frequency in kHz,
and T is temperature in *C.
Employing equation (7) with complex sound celerity to
account for observed attenuation, variation in the value
of the reflection coefficient occurs relative to that
found employing solely real number celerities. The region
to the left of the critical angle (8crit) is affected by
the compressional speed attenuation (a) and angles larger
than @crit vary due to alterations in the shear speed
attenuation (). The value of 8 crit, however, does not
change, and the angle still represents a local maximum of
the reflection coefficient, but that value may no longer
be unity.
Brekhovskikh (1980) expands the Clay and Medwin
approach further by considering a layered medium of finite
thickness bounded by two half spaces. This model more
closely represents the Arctic environment. His pressure
reflection coefficient is defined as:
RP = M (ZI - Z3) + i [(M2 -N 2 ) Z1 + Z3]
M (Z1 + Z3) + i [(M2 - N2) Z1 - Z3]
when the following are true:
Z= (p, cl)/cos (81) Z2= (p2 cp2 )/cos (8 2p) (9)
Z2t= (P2 c. 2 )/cos (82s) Z3 = (P3 c 3 )/cos (83)
M = (Z2/Z 1 ) cos 2 (282,) Cot (P) + (Z2 t/Z 1 ) sin2 (22) cot (Q)
67
N = {Z2 cos 2 (2) 2,)/Z 1 sin(P)} + (Z2t/Zi) sin2 2@2s/Zl sin(Q)
P = k2 h cos (8 2p) Q = K2 h cos (82)
k 2 = 2 f /Cp 2 K2 = 2 i f /c1 2
h = layer thickness (m)
When adapting equation (9) to the Arctic environment
Brekhovskikh obtains a reflection coefficient of unity for
all angles. This conclusion is substantiated by McCammon
and McDaniel (1985) using the Thompson-Haskell matrix
method. Using the values for the acrylic model, a value
of one is likewise obtained (Figure 16). HoweveL, this
does not correspond to real world or laboratory data, a
disparity noted by McCammon and McDaniel, as well. The
means of solving this incongruity is the inclusion of
attenuation into the equation by employing complex sound
speeds.
When applied to equation (9) as per McCammon and
McDaniel (1985) complex sound speeds and attenuation
produce reflection coefficient values less than one. Two
samples of the variation this causes are found in Figures
17 and 18.
D. EXPERIMENTAL DATA AND CONCLUSIONS
Fiqures 19(a) through 19(f), show equation (7) solved
for the appropriate frequency and employing the
attenuation factors as respectively noted, with
68
ON
'-4
E-4E-4<r.
E.-,
N CO
00
C)
E-4
P-4 -
C/3)
.Figure 16. A plot of Brekhovskikh's three-layer.
equational model for the pressurereflection coefficient employinlaboratory values
69
°N \
0
-Cn
OCx
C a)
Z:o
C
- E"
Figure 17. A depiction of Brekhovskikh's equation
(9) with a = -60, P = -600 and a fre-quency of 123.06 kHz
70
0
XM
x
(.0.--.- 4
: .
E-E- 0-4
q4
N1-
0 zE-E- 0 ~ : -
Figure 18. A plot of Brekhovskikh's equation (9)with a = 125, 1 = 400 and a frequencyof 80.08 kHz
0
0
~0-
C-,3co -
CLI tC
P4 - C
0L.0
C0 MC4
aVEL~CL
C/3)
a~~~& Ad a * *0~~4~4~~0Ev 00 - OQ4E-
72
0
.2
a0
C3
C-- )
rL4L
E-4-0- = 0
'.0
E-4 [W
a.
LIL
r4 U 4040
0Z
C-) 0Z 'a>
E-E=2:L X
ca0-
6 bJ3 '4! C5
- . .. a a aMPZ4 P .- I W C; E 00c ~ Z14- 0 -.J P4:E-
73
0
cn 0cca
t-4
CE
0
r* II
c3- .0
C4ra CA C
[-0-- 008
Q~ E
C> rX4 > o.
[0w-I2:.o
-co0.0) coCL I
o c
=00
1C >
ra -V- cr c - th. U 4 "J c ) N~i C3 m .
P -r.. Q 7,z-4 4 : E- LL
74
-% 0
L co
0-0
C-- .0
LWC1
ca c
r1a.9: 4 m2 t.
0 C3
oC t>43
o a 0
<r 0w-C3 4) CL
0X CL 0 0
P-4
oo
0
V4 ccn co r- %D m-.~r .7 E . .
75
o- 0
a% 0
'4 003ciCO [-
a) 0
C.3 C3 V
r-84 < - 0
L. I0.L.
~.C2':40
E-4 00
':144
CLo
v: '::4 0
C~CO
<r. - a 0*j
r:4o= C ,O '0
-10. CL
P:4
. . ..3
76
0
0 '
0~ 31
COSa,-
C4C C a
C
CIO0'-- CL
C4 -I CL
CL (
E-) 030)0
E- C4
C2>
N, ~ a~ C3
.0a)0 3:10
-- 1" -E "
'a.
M PL co rC4
0 ,. :co C5.0 ;
'. >c o
o, .
P 'L ' w.-E'1 =
CA , . ,-3
77
experimentally derived data points superimposed for each
of the six frequencies of interest. A strong correlation
is noted between the theoreticl and experimental values.
The "error bars" denote the high and low experimental
values and the range within which the values fell, with
the circle denoting the average value.
a was determined to be .003f and P was found to beequal to 1.5f (both with f in kHz and units of (m kHz) -l)
in the laboratory acrylic, using a variety of coefficients
to obtain a best fit. These values differ from those
reported by others. Denny and Johnson present {.424f and
.853f) in dB/m with f also frequency in kHz, and Browne
the same for their acrylic. McCammon and McDaniel present
{.06f(-6/T)2/3 and .36f(-6/T)2/3} also in dB/m when T is
temperature in "C, for Arctic ice.
The values of reflection coefficients (both the
theoretical and laboratory data) correspond closely with
the real world data reported by Langleben (1970) and
McCammon and McDaniel (1985). The literature reported
Arctic data has been plotted on the 287 kHz graph as this
is the frequency that is most appropriate given the known
scaling parameters. Langleben's 17.9 kHz would be
represented by 6.93 MHz in the laboratory model (and is
represented by stars on the graphs) and McCammon and
McLaniel's 625 Hz corresponds to 276.8 kHz (and is
depicted by triangles).
78
Poor correlation exists between Brekhovskikh's theory
with the addition of attenuation effects and the data from
all experiments. The fact that experiment and theory do
not agree is corroborated by Diachok and Mayer (1969).
They note additionally, that losses in reflectivity may be
caused by conversion to a Rayleigh-type wave where
reflection is conical in nature rather than totally
reflected. This would account for poor agreement at
angles near ecrit-
Finally there is undoubtedly some error in the
collected data as any temperature variations were not
accounted for and McCammon and McDaniel define attenuation
as temperature dependent. Further, chemical impurities
existing in the water also result in alteration of
acoustic response. Rust, fiberglass and simple dust
accumulation could have altered the water properties
sufficiently to disturb the experiment. Despite this,
there is strong agreement between experimental data, the
Clay and Medwin theoretical plot when their equation is
altered to account for attenuation losses, and scaled
reported data, particularly that of Langleben.
79
V. ACOUSTIC SCATTERING
A. THEORETICAL FOUNDATIONS
To begin the study of scattering phenomena Huygen's
principle is once again invoked. Treating each distinct
parcel of the ensonified object as a re-radiating point
source and summing the wave fronts gives an excellent
visual model of the scattering process. The effect in
this instance, due to the roughness of the object, is
energy loss in a variety of directions. The energy of a
signal that is normally incident will no longer be
reflected exclusively back at the source (Figure 20).
Thus, the value of the scattering coefficient will be a
function of a myriad of variables, among which are several
distinct angles (incidence, object orientation or aspect,
direction of interest for scattered wave amplitude) as
well as some form of representation of the amount of
surface roughness present. This experiment is concerned
with that portion of the incident energy which is
scattered in the original direction of propagation and
thus continues its travel; this is termed forwardscatter.
B. ADDITIONAL ENVIRONMENTAL PARAMETERS OF IMPORT
Several additional parameters become important to
consider when expanding the simple, smooth, plane surface
Arctic model to include large--sca', roughness factors.
80Huygen's Principle Applied To Scattering Phenomena
P I
.04-0ClwUCL
h4.
CC
0(D
C)O
0)0
cro
0L)E0
0
Figure 20. Huygen' s principle when applied to thescattering phenomena on a rough-surfacedobject. (Clay and Medwin, 1977)
81
The most obvious of these variables is pressure-ridge keel
depth (h), the probability density of which may be modeled
by:
(2abh + ac) e - (abh^2 + ach)
where a = the proportionality constant, b = A/h2, A =
cross-sectional area, h = keel depth, c = n h/8 f Ro,
= mean keel spacing, R, = 1.6 or half-width-to-depth
ratio (Greene, 1984).
Ridge orientation is another key factor that must be
considered. Although it is commonly assumed, for the
purposes of modeling, that ridges are directionally
isotropic, statistical analyses indicate that in certain
regions there may exist a preferred direction for keel
orientation (Greene, 1984). The relative probability that
a given ridge link of length L will cross the path of
concern, is proportional to the length of the projection
in the direction perpendicular to the track, L sin(@),
where 8 is the angle between the axis of the ridge and the
track. The probability density for the angle of
intersection of ridges crossing the track is:
(1/2) sin(O) dO, for 0., 9 < n
with the associated distribution function:
82
(1/2) (1 - cos(8)) (Greene, 1984).
The "apparent width" of the ridge is a function of
the aspect from which the object is viewed. The apparent
width is defined as:
Wa = W / sin 8
where 8 is the angle of intersection between the axis of
the structure and the measurement track. Wa will have a
distribution of:
4(l - (W/Wa) 2 on [W,-]
and a density given by:
W2/(Wa 2 4 (Wa2 - W 2)) dWa.
Lead edges add further scattering surfaces. In
Wadhams (1981) the number density of leads per kilometer
of observed width d meters was found to obey a power law:
n(d) = 15 d- 2
where a lead was defined to be a continuous sequence of
depth points, greater than 5 meters long and not exceeding
83
1 meter of draft, as observed from the perspective of an
upward-looking sonar. Greene (1984) states that the
density for actual lead width is in fact:
p(W) = (1/W,) e -W/wo.
Coherent scattering loss formulae and scattering
loss kernels for the incoherent field based on statistical
techniques require the autocorrelation for input. In
order to calculate the autocorrelation for a rigid
surface, one may employ discrete ridge statistics and a
specified ridge shape or ensemble of ridge shapes.
C. THEORIES OF SCATTER EFFECTS
The amount of scattering that occurs to the energy
incident on an object is partially a function of the
wavelength of the waves in question; it is a frequency-
related response. Due to this phenomenon the nature in
which an object's roughness is described is related to the
wavelength of the incident energy. One model of the
relative measure of an object's roughness is the Rayleigh
parameter (R) which is defined as:
R = k * H * sin(8) (Urick, 1983)
where k is the wave number (2xf/c), H is the root mean
84
square (rms) "roughness height" and 8 is the grazing angle
of the impinging acoustic wave. For values of R << 1 the
surface is defined as a reflector (i.e. it is
"acoustically" smooth); and when R >> 1 the object is a
scatterer (i.e. rough). Thus, an acoustic wave interacts
with an object as rough or smooth relative to its own
wavelength.
An amplitude reflection coefficient for an irregular
surface is defined by Urick (1983) as:
= exp (-R)
when R is the Rayleigh parameter as defined as above.
Thus, the amount of energy forwardscattered will decrease
with increasing frequency or grazing angle (the complement
to the incident angle) for any given object. This fact is
noted by Denny and Johnson (1986) and Brekhovskikh (1982).
Gordon and Bucker (1984) confirm that scattered energy
decreases with increasing frequency and increasing
roughness. Greene demonstrates increased scattering
losses as a function of increased range and frequency.
Brekhovskikh derives an equation for the amount of
energy scattered in the forward direction, which he
denotes "coherent reflection in the specular direction".
He begins with the energy conservation law as applied to
the energy of the incident waves. This generates:
85
R = 1 - 2 * k * cos (8o) fG(x) [k2 - (po + x) 2 ]1 / 2 dx
where k is the specific wave number, Bo is the specific
angle of incidence, G is the Fourier transform of the
correlation function, x = {x cos(a), x sin(W)} and is the
Fourier representation of the wave number when a is the
azimuth angle, e. is the horizontal component of the wave
vector, and T, defines the region over which the integral
is to be taken - in this instance the range is defined for
x as 0 to - and for a as -n to n. Through algebraic and
integrational simplification when applied to the situation
of large scale roughness (such as that present in the
Arctic) this becomes:
R = 1 - R2/2
where R is the Rayleigh parameter as previously defined
(Brekhovskikh, 1982).
The Science Applications International Corporation
(SAIC) has developed a scaling model for the Arctic
environment, termed the SAIC Interim Scattering Model for
Ice or SISM/ICE. The standard deviation of roughness is
the only parameter that the model requires for
predicLions. It is valid for acoustic waves with
frequencies from 0 to 5000 Hz and grazing angles of 0 to
45 degrees. The under-ice surface is considered to be
86
flat with the pressure-ridge keels modeled as cylindrical
bosses of elliptical cross-section. The following
assumptions regarding the bosses are made:
1) they have a half-width-to-depth ratio (Ro)
of 1.6
2) they have a Rayleigh depth distribution
3) they have a random orientation
4) they exhibit random spacing along a track
Under-ice roughness spectra measured along a track
may be approximated by a two-parameter spectral model. The
standard deviation of roughness (a) derived from such a
spectrum is:
02 = 2c/02
where P is the regression coefficient for the population
(Greene, 1984).
The SISM/ICE model is a hybrid of scattering theories
based upon both continuous and discrete roughness models.
Mean ridge spacing (Q) is assumed to be 100 m for the
purposes of this model. All angles 0 are grazing angles.
Four formulae are given. The predicted value of R is the
maximum of the four calculated values.
Low Frequency-Free Surface Formula
R = (1 - 4 sin(0) k2 02 (1-n c sin(6)/2))1 /2
87
High Frequency-Free Surface Formula
R = (I - 4 sin(8) (1.198) c (k/0) 3 / 2 )1 / 2
High Frequency-Rigid Surface Formula
R = ([sin(@) - x] 2 + x2)/([sin(e) + x] 2 + x2 ) x < sin(@)
(.2)1/2 x > sin(e)
where x = 1.311 c (k/P)1 / 2
Asymptotic Twersky Formula
R = [sin(8) - x]/[sin(e) + x]
where x = n L cos(8-) tan (T) = p- 2 tan (6)
L2 = W2 (tan2 (e) + p4)/(tan2 (e) + p2 )
w = Ro n h/2 p = 2/(Ron) n = 1/0 (Greene,1984).
D. FORWARDSCATTER DATA AND CONCLUSIONS
The majority of studies consulted are concerned with
backscatter data, as this is the portion of the acoustic
energy budget which negatively affe.ts the operation of an
active sonar. Reverberation masks the sonar's ability to
detect the desired echo signals and is caused.by
backscatter towards the source. However, this experiment
studies the reflection and fPrwardscatter suitable for
lonJg-,ange propagation effcts. Thus, the abil t1y to
compoare t... experimentally determined forwardscatter data
88
with that from other models and studies was somewhat
limited.
Denny and Johnson (1986) report data collected from
three grazing angles at fourteen different frequencies
ranging from 31.3 to 82 kHz. Their data correspond to
39.1 to 102.5 kHz when scaled to fit the parameters of
this experiment. Their mean values of scattering loss per
bounce are presented on Figure 21 and shows the expected
frequency and angular dependence.
The SISM/ICE model reports theoretical transmission
loss as a function of range and compares that to real
world data (Figure 22). Similar reliance is again
exhibited upon frequency in both their theoretical and
experimental data.
Gordon and Bucker (1984) present environmentally
obtained data in terms of scattering loss per bounce in
Figure 23, which is the same format as Denny and Johnson.
The same angular and frequency variation is evident in
their data and consistent with theory. Gordon and
Bucker's Arctic frequencies correspond to frequencies of
39.7 and 79.4 kHz in the laboratory.
This experiment determined a scattering ratio,
defined as the ratio of forwardscattered peak pressure
amplitude to direct path peak pressure ampitude. The
manner of collection followed was as outlined in the
Procedure chapter, for five angles of incidence at six
89
On
03
01
0CO,
o--
14
o N
"': N -" CO :).e C
.-1
I N M V 1 I -I 1 1 a)
Figure .21. Mean values of scattering loss perbounce as reported by Denny and Johnson(1986)
90
Environmental and Theoretical Transmission Loss Data for
a Rough Surface
70
-4'W
1100 KI
K 50Hzf
6- Ito
120 10 so M0 ISO 200 250 300 4s0
RANGE (Wn~
Figure 22. A plot based oni a simulated ice surfaceconsisting of equal depth, equallyspaced trapezoidal ice keels, trans-mission-loss &ata from a Central Arcticsite at 40 Hz (C.... ) and 50 Hz (xxxx)compared with simulated transmission-loss at 40 Hzi C... and50 Hz ( ---- )tusing the Arctic High Angle Parabolic! erration. (Greene, 1984)
91
Environmentally.Collected Reflection Loss Data
.0
W
w-,J
0A*
0 10 i0
GATI&G ANGLE (w)
Figure 23. Ice reflection losses as a function of
grazing angle at two frequenC.ies as
used in the Arctic propagatio.n prOgram.%he losseb axe due to .scatterilg except
that part over the shaded areal which is
due to ice loss (Gordon and Bucker, 1984)
92
separate frequencies. This data are plotted in terms of
deciBels (dB) on Figure 24 and responds as anticipated.
There is some lack of agreement in the extremely high
frequency range; at these frequencies large-scale
scattering effects occur due to the increased relative
size of the keel. Birch (1972) mentions what may have
been an additional problem: at frequencies when the
surface is "acoustically rough" (i.e. high frequencies),
the exact angle of impingement is uncertain, thus
prediction of scatter strengths as a function of grazing
angle is difficult.
Further, data in this experiment as well as that of
Denny and Johnson were collected solely for one
"statistically correct" keel, rather than an
environmentally correct ridge field as in Greene's
reported data. The Gordon and Bucker data are derived
from a field of keeis but analyzes only one bounce or
reflection. This may account for the fact that the losses
are up to 40 dB greater for Greene's reported data as
compared to the other experimental v"iues of both the
laboratory and environment.
Some of the data disparity may also be accounted for
by a return to the Rayleigh parameter. For those
frequencies chosen in this experiment and an rms roughness
height for the keel of .0163 m, the following conclusions
are obtained:
93
C,))CO)0
bE-4
E-4'
CO)
:> -.0
<C Cr 0
914.X~
to 0: 3n~
I. I3 ~ 4 C-4 0- C!1 Wt C! O'atdo op V-CM .0
Figure 24. Experimentally derived data for scatteringloss per bounce
94
20.50 kHz demonstrates smooth surface effects
61.52 kHz are in the undefined region, not80.08 kHz acoustically smooth or rough
123.06 kHz
205.08 kHz demonstrates rough surface effects287.00 kHz
Thus, the fact that the 20.50 kHz data follows closely
that of the reflection data and does not demonstrate
large-scale losses is expected. Likewise, the 61.52,
80.08, and 123.06 kHz data fall within the region defined
by Rayleigh as exhibiting properties of both. The 205 and
287 kHz are the only frequencies that actually fall within
the Rayleigh parameter for roughness foi the majority of
the angles involved in the experiment. There exists a
strong qualitative correlation of frequency and grazing
angle dependence between theory and all data. Finally,
when comparing this experiment with Denny and Johnson, and
Gordon and Bucker (which share similar analysis
techniques), quantitative values for scaled frequencies
are extremely close.
95
VI. SUMMARY OF FINDINGS
This paper has presented a series of experiments that
modeled the acoustic-ice interactions using burst
transmissions from omnidirectional underwater point
sources. Floating acrylic plates were employed to
represent the Arctic ice due to the similiarity in
impedance characteristics and other physical properties to
known ice values. Geometrical properties of the ice were
accurately scaled in the acrylic by maintaining the
appropriate wavelength ratios. Reflection and
forwardscatter effects were analyzed and compared with
existing theories for the Arctic. Six frequencies were
utilized to gather data for both reflection and scattering
effects.
The equation presented by Clay and Medwin (1977) for
reflection at a liquid-solid interface was modified by the
addition of attenuation factors through the use of
complex sound speeds. A strong correlation between the
revised theoretical and obtained experimental values of the
reflection coefficient was noted.
Compressional wave speed attenuation (a) in the
.0063 m sheet of PlaskoliteTM acrylic utilized in this
project was determined to be .003f (f in kHz) and a shear
attenuation (P) was found to be equal to 1.5f (f in kHz)
with units of (m kHz)-1 . These values differ from those of
96
others. Denny and Johnson report .424f and .835f in dB/m
(f in kHz) for their acrylic, Browne {same) and McCammon
and McDaniel {.06f(-6/T) 2/3 and .36f(-6/T)2/3} dB/km kHz
for ice.
The values of reflection coefficients (both the
theoretical and laboratory data) correspond closely with
the real world data reported by Langleben (1970) and
McCammon and McDan.al (1985) when scaled to the frequencies
appropriate to this experiment.
Poor correlation exi-%s between Brekhovskikh's theory
(with or wit.,at the addi'.ion of attenuation effects) and
the data from all experiments. The fact that experiment
and theory do not agree is noted by Diachok and Mayer
(1969). They have noted additionally that losses in
reflectivity may be caused by conversion to a Rayleigh-type
wave where reflection is conical in nature rather than
totally reflected. This would account for poor agreement
at angles near Ocrit-
Additionally, there is undoubtedly some error in the
data collected, as variations in temperature were not
accounted for and McCammon and McDaniel define attenuation
with a temperature dependence. Further, chemical
impurities existing in the water, such as dust, debris and
rust that had entered the tank, could also result in
alteration of acoustic response. Despite this, there is
strong agreement between experimental data, the Clay and
97
Medwin theoretical plot when the equation has been altered
to account for attenuation losses, and scaled reported
data.
Strong frequency and grazing angle dependence was
noted in the scattering data, as anticipated. There is
some lack of agreement in the higher frequency range; at
these frequencies large scale scattering effects occur due
to the increased relative size of the keel. Further, data
was collected solely for one "statistically correct" keel,
rather than an environmentally correct ridge field. Good
agreement exists both qualitatively and quantitatively
between the values for this experiment, Denny and Johnson's
experimental values, and Gordon and Bucker's environmental
data.
Further study is required into the acoustic
interaction in the colloidal region; research into its
modeling will prove beneficial to future understanding.
Additional attempts to improve Brekhovskikh's
environmentally correct three-medium mathematical model to
better fit Arctic data and thereby generate a means of more
accurately predicting reflection response will prove
extremely important. Investigation of acoustic attenuation
in various media will supplement the overall comprehension
of reflection and transmission phenomena as well.
Continued collection of real world information is also
necessary to expand the database and provide insight into
98
the specific governing factors of the acoustic propagation
phenomenon. The Arctic remains a region of complex
acoustic interactions and it is only through continued
diligent study that it will be possible to successfully
conquer this scientific frontier.
99
REFERENCES
Ackley, S. F. et al., 1976, "Thickness and RoughnessVariations Of Arctic Multiyear Sea Ice", Cold RegionsResearch and Engineering Laboratory Report 76-18, TableII.
Birch, W.B., 1972, "Arctic Acoustics in ASW", IELFEInternational Conference on Engineering in the OceanEnvironment Record, Institute of Electrical andElectronic Engineers, Inc., NY, NY, p. 293-297.
Brekhovskikh, L. and Yu. Lysanov, 1982, Fundamentals ofOcean Acoustics, Springer-Verlag.
Brekhovskikh, L., 1980, Waves in Layered Media, AcademicPress, Inc.
Browne, M. J., 1987, "Underwater Acoustic Backs,atter froma model of Arctic Ice Open Leads and Pressure Ridg,-.;",Naval Postgraduate School, Monterey, CA.
Bunney, R. E., 1974, "Feasibility of acousticallydetermining the thickness of sea ice", Applied PhysicsLaboratory, University of Washington.
Clay, C. S. and H. Medwin, 1977, AcousticalOceanography: Principles and Applications, Wiley &Sons.
Covault, C., "Soviet Ability to Fire Through Ice CreatesNew SLBM Basing Mode," Aviation Week and Space Technology,December 10, 1984, pp. 16-17.
Denny, P. L., and K. R. Johnson, 1986, "UnderwaterAcoustic Scatter from a Model of the Arctic Ice Canopy,"Naval Postgraduate School, Monterey, CA.
Diachok, 0. I., and W. G. Mayer, 1969, "Conical Reflectionof Ultrasound from a Liquid-Solid Interface," ._ uSoc, Am., 47 (1), pp. 155-157.
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APPENDIX
There were two primary computational obstacles at the
outset of the experiment. The first was separating the
desired return signal from the myriad of extraneous echoes.
These undesired reflections would occur due to the confines
of the relatively small tank within which operation of the
model occurred. Rather than employ a filtering or gating
system which might distort the return data, it was decided
that the desired pulse would be manually (i.e. visually)
extracted from the return. In order for this to be
performed it was necessary to calculate a "window" within
which the reflected pulse could be anticipated. Further,
knowledge of the time that the other reflected pulses would
be arriving would serve to help elucidate the "signal" from
the "noise", or more accurately, the one desired reflection
from those not desired.
The second problem was a lack of data on the
particular acoustic parameters governing the acrylic sheet.
The specifications provided by the acrylic manufacturers
were obviously not acoustic in nature. It was thus
necessary to apply the known data with the aid of several
equations to determine the characteristics of the acrylic
and describe the model in a more appropriately acoustical
fashion.
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The Universal Technical Systems, Inc. TK Solver PlusTM
equation processor software was employed to solve these
problems. It. utilizes a declarative or rule-based
programming language that permits direct input of a series
of equations and subsequent analysis of the effects of
either single or multiple variable manipulation. "TK"
stands for "tool kit" and is an excellent description of
the utility of the software (Frank 1988).
Specifically in this experiment, the parameters of
hydrophone placement and tank dimensions were entered.
Through the use of a simple array of trigonometric
equations the angles, distances, and time windows of
interest were calculated. The software saved numerous
hours of hand computation of there values. Additionally,
the use of this technique enabled the data to be collected
free from filtering or gating devices as time separation of
the incident pulse from the various reflections was
ensured. This allowed for a "purer", less technically or
electronically distorted signal and therefore more accurate
data and conclusions.
Limited data were available regarding the acrylic
parameters for the laboratory. Seeking theoretical values
with which to compare those determined experimentally, the
following derivational method was employed. Given a
specific gravity from the PlaskoliteTM Properties Sheet and
taking a value of water density of 998.84 kilograms/cubic
104
meter (kg/m3), the density of acrylic was determined to be
1189.8 kg/m 3. The sheet also provided a bulk modulus of
elasticity of 449,000 pounds per square inch. Conversion
of this value to mks units resulted in 3.097 X 109
Newtons/m2. The technical information available however
extended no further. Employing the TK Solver PlusTM
program, which allows for iterative analyses, the remainder
of the acrylic parameters were determined theoretic.lly.
This employed the following four equations and the two
known values to solve for the four unknown parameters:
o (sigma) - Poisson's Ratio E - bulk podulus of elasticity
G - bulk modulus of rigidity p - density of acrylic
c - compressional wave speed c. - shear wave speed
in acrylic in acrylic
= [3E - p * c 2 ]/[3E + p * c 2 ] a
c2 = [E + 4/3* G]/ p a
E =2 * (1+) * G b
C32 = G/p a
105
This provided the following values:
c = 1939.0273 meters/second c. 931.47804 rn/s
a = .5000258 G =1.03233 X 109 N/rn2
E = 3.097 X 109 N/rn2 p =1189.8 kg/rn3
a - (Clay and Medwin, 1977)
b - (Gere, 1984)